Concurrent electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) bridge brain connectivity across timescales. During concurrent EEG-fMRI resting-state recordings, whole-brain functional connectivity (FC) strength is spatially correlated across modalities. However, cross-modal investigations have commonly remained correlational, and joint analysis of EEG-fMRI connectivity is largely unexplored. Here we investigated if there exist (spatially) independent FC networks linked between modalities. We applied the recently proposed hybrid connectivity independent component analysis (connICA) framework to two concurrent EEG-fMRI resting-state datasets (total 40 subjects). Two robust components were found across both datasets. The first component has a uniformly distributed EEG frequency fingerprint linked mainly to intrinsic connectivity networks (ICNs) in both modalities. Conversely, the second component is sensitive to different EEG frequencies and is primarily linked to intra-ICN connectivity in fMRI but to inter-ICN connectivity in EEG. The first hybrid component suggests that connectivity dynamics within well-known ICNs span timescales, from millisecond range in all canonical frequencies of FC EEG to second range of FC fMRI . Conversely, the second component additionally exposes linked but spatially divergent neuronal processing at the two timescales. This work reveals the existence of joint spatially independent components, suggesting that parts of resting-state connectivity are co-expressed in a linked manner across EEG and fMRI over individuals. Author Summary Functional connectivity is governed by a whole-brain organization measurable over multiple timescales by functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). The relationship across the whole-brain organization captured at the different timescales of EEG and fMRI is largely unknown. Using concurrent EEG-fMRI, we identified spatially independent components consisting of brain connectivity patterns that co-occur in EEG and fMRI over subjects. We observed a component with similar connectivity organization across EEG and fMRI as well as a component with divergent connectivity. The former component governed all EEG frequencies while the latter was modulated by frequency. These findings show that part of functional connectivity organizes in a common spatial layout over several timescales, while a spatially independent part is modulated by frequency-specific information.